We give a structural characterization of linear operators from one C*-algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a V-isomorphism, such a map admits of a decomposition into a degenerate and a non-degenerate part, the non-degenerate part of which appears as a Jordan V-morphism followed by a``rotation'' and then a reduction. In the case of maps whose adjoints preserve pure states, the degenerate part does not appear, and the``rotation'' is but the identity. In this context the results concerning such pure state preserving maps depend on and complement those of Sto% rmer [1963, Acta Math. 110, 233 278, 5.6 and 5.7]. In conclusion we consider the action of maps with``extreme point preserving'' adjoints on some specific C*-algebras. 1998Academic Press

Abstract. The celebrated Gauss-Lucas theorem states that all the roots of the derivative of a complex non-constant polynomial p lie in the convex hull of the roots of p, called the Lucas polygon of p. We improve the Gauss-Lucas theorem by proving that all the nontrivial roots of p lie in a smaller convex polygon which is obtained by a strict contraction of the Lucas polygon of p.

ABSTRACT. The aim of this paper is to characterize those linear maps from a von Neumann factor A into itself which preserve the extreme points of the unit ball of A. For example, we show that if A is infinite, then every such linear preserver can be written as a fixed unitary operator times either a unital Ł-homomorphism or a unital Ł-antihomomorphism.

It is proved that every function of finite Baire index on a separable metric space K is a D-function, i.e., a difference of bounded semi-continuous functions on K. In fact it is a strong D-function, meaning it can be approximated arbitrarily closely in D-norm, by simple D-functions. It is shown that if the n th derived set of K is non-empty for all finite n, there exist D-functions on K which are not strong D-functions. Further structural results for the classes of finite index functions and strong D-functions are also given.

No abstract